Precision Top Mass Measurements vs. Yukawa Unification Predictions

Abstract

How accurately should the top quark mass be measured in order to test theoretical predictions? A possible answer is presented within a particular theoretical framework, that of top-bottom-tau Yukawa unification in a supersymmetric SO(10) grand unified theory. Yukawa unification, and the uncertainties in its $m_t$ prediction, are introduced by analogy to gauge unification and the uncertainties in the predictions of $sin^2\theta_W$ or $\alpha_3(m_Z)$. There are two sources of uncertainty in this framework: ``removable'' uncertainties due to physics at the electroweak and supersymmetry-breaking scales, and ``irremovable'' ones from physics at and above the unification scale. The latter are precisely the model-dependent effects which would shed light on the nature of the unified model, so they may be regarded as a (model-dependent) part of the prediction rather than as uncertainties. The removable sources are estimated first using current experimental bounds, and then using plausible guesses for the bounds that may be available within roughly a decade: they are not likely to be reduced below roughly $\pm 1 GeV$. That is the level at which such unified theories will be testable against future experimental determinations of the top mass.